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Tsinghua Science & Technology

Quantum switching based on the nearest neighbor hamiltonian

Min Jiang, Xu Huang, Yiming Zhou

Published Feb 1, 2011• 0 citations
Publisher

Abstract

This paper describes a quantum switching architecture for nearest neighbor coupling. An efficient quantum shear sorting (QSS) algorithm is used to reduce the number of time steps. For the QSS algorithm, the running complexity of the quantum switching architecture is polynomial in time with the nearest neighbor coupling and the implementation is less complex. The result shows that improved switching is extremely simple to implement using existing quantum computer candidates.

DOI
10.1016/s1007-0214(11)70016-5

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This paper describes a quantum switching architecture for nearest neighbor coupling. An efficient quantum shear sorting (QSS) algorithm is used to reduce the number of time steps. For the QSS algorithm, the running complexity of the quantum switching architecture is polynomial in time with the nearest neighbor coupling and the implementation is less complex. The result shows that improved switching is extremely simple to implement using existing quantum computer candidates.
In this paper, we propose a quantum switching architecture under the nearest coupling limitation. In order to reduce implementation time steps, an efficient quantum shear sorting (QSS) algorithm is developed. With use of QSS algorithm, the running complexity of the improved quantum switching architecture is polynomial time even under nearest coupling interaction and the implementation complexity is better. Our improved switching is extremely simple to implement by existing quantum computer candidates.
This paper proposes a quantum switching architecture that can dynamically permute each input quantum data to its destination port to avoid using the fully connected networks. In addition, in order to reduce the execution time of the quantum switching, an efficient quantum merge sorting (QMS) algorithm that provides a parallel quantum computation is also developed. The quantum switching utilizes the QMS algorithm as a subroutine so that the total running time can be reduced to polylogarithmic time. Furthermore, to evaluate the feasibility of the quantum switching, we also define three different kinds of performance factors that can be used to estimate the complexity in implementation and the time delay in execution for quantum instruments. From the evaluation results, it can be seen that the proposed quantum switching is feasible in practice.
Several promising implementations of quantum computation rely on a Linear Nearest Neighbor (LNN) architecture, which arranges quantum bits on a line, and allows neighbor interactions only. Therefore, several specific circuits have been designed on an LNN architecture. However, a general and efficient conversion method for an arbitrary circuit has not been established. Therefore, this paper gives an efficient conversion technique to convert quantum circuits to an LNN architecture. When a quantum circuit is converted to an LNN architecture, the objective is to reduce the size of the additional circuit added by the conversion and the time complexity of the conversion. The proposed method requires less additional circuitry and time complexity compared with naive techniques. To develop the method, we introduce two key theorems that may be interesting on their own. In addition, the proposed method also achieves less overhead than some known circuits designed from scratch on an LNN architecture.
A novel quantum learning method is presented,which combines quantum computation with classical K-nearest-neighbor,called quantum K-nearest-neighbor.Its steps are introduced in detail.Further,in order to save to running time of quantum counting subroutine,the fired K is revised to the changeable K.Under the framework of Boosting algorithm,a strong classifier is build,which consists of three weak classifiers,each trained by the quantum k-varying nearest neighbor,to improve the performance of classification.In this algorithm,the time complexity of classical K-nearest-neighbor algorithm is reduced from O(N) to O(N) by means of the power of quantum algorithms.
Design and synthesis of quantum circuits have gained huge momentum during the last few years. With various physical constraint sone of the major issues is in making quantum circuits nearest neighbor complaint. The existing one and two dimensional architectures for the placement of qubits does not scale well for larger circuits. The situation thus demands for a faster approach to solve the problem. To make a quantum circuit nearest neighbor compliant, SWAP gates are inserted in the quantum gate circuit to bring the interacting qubits of a gate adjacent. We have proposed a faster method with a simple yet effective algorithm to minimize the number of SWAP gates for adjacent interactions. The time required for processing does not exceed one second even for larger benchmark circuits. The proposed method is found to reduce the number of SWAP gates on an average by 9.5% compared to the best results in previous works on 2D architectures, and by 45.7% compared to the best results on 1D architecture.
Abstract In some quantum technologies, an interaction is only allowed between physically adjacent qubits, hence the nearest-neighbor requirement is needed. In such technologies, quantum gates are limited to operate on adjacent qubits. To make a quantum circuit compliant with the nearest-neighbor requirement, SWAP gates are inserted into the circuit to move the interacting qubits of a gate to be adjacent to each other. The mapping of qubits on the physical environment has an important role on reducing the number of SWAP gates and thus the circuit latency. Focusing on this issue, in this paper, a method is proposed that maps a quantum circuit onto a 3D physical hardware such as a 3D optical lattice. A new methodology for this mapping problem is proposed based on a complex network spectral clustering algorithm and graph theory, which are suitable for very large scale networks. It includes three steps: finding the order of qubit mapping, placing physical qubits, and routing. Simulation results show that the proposed mapping approach not only decreases the average number of SWAP gates by about 37% but also improves the average runtime by about 87% for the 2D architecture compared to PAQCS. Moreover, it reduces the average number of SWAP gates for the 3D architecture by 17.1% compared to the best studies in the literatures.